Answer:
1. 
2. 
Explanation:
Given:
- mass of block,

- spring constant,

- maximum velocity of block,

1.
<u>We know from the energy of oscillating spring:</u>



2.
Now, given that:
instantaneous position, 
we find angular speed,



So we have



gravitational Potential energy is given by

here we have
m = 200 kg
h = 21000 m
now we will have


so GPE of balloon will be 41160000 J above the given height from ground
Answer:
C. Mass is independent of the force acting on the mass.
Weight depends on the gravitational force acting on the mass.
Example: A mass of 1 kg on the earth still has a mass of 1 kg on the moon;
whereas the weight of that mass on earth is 9.8 N and only 1/6 of that amount on the moon.
The answer is 56.98 m
The dislocation (d) is:
d = v1 * t + 1/2 * a * t²
v1 - initial velocity
t - time
a - <span>acceleration of gravity
We know:
d = ?
v1 = ?
t = 6.82 s / 2 = 3.41 (it reaches the peak at half time)
a = - 9.8 m/s</span>²
Let's first calculate v1:
v2 = v1 + at
v2 - final velocity (v2 = 0 when it reaches peak)
0 = v1 + -9.8 * 3.41
0 = v1 - 33.418
v1 = 33.418 m/s
d = v1 * t + 1/2 * a * t²
d = 33.418 * 3.41 + 1/2 * -9.8 * 3.41²
d = 113.96 - 56.98
d = 56.98 m
To solve this we are going to use the formula for work:

where

is the work done

is the force

is the distance
Scenario A. We know for our problem that

and

. Lets replace those values in our formula to find

:

Scenario B. We know for our problem that

and

. Lest replace those value in our formula:

Scenario C. We know for our problem that

and

. Lets replace the values in our formula:


We can conclude that:
- The scenario that requires the most work is
C.
- The scenario that requires the least work is
A.